"The 1% now partner will receive monthly payments from the new 99% partner.  I wasn't sure how to treat the payments to the now 1% partner."

If you sold me your shares of Ford, nothing changed at Ford.

Again, it depends on which return you are working on. You seem to have a partner selling his share at $0, and absent other partners, that would become a single-member LLC as disregarded entity. Instead, he turned around and sold 99% under an installment sale.

Meanwhile, the partnership, as its own entity, is not changed. Nothing happened here.